Research:
Automated Modeling
Research:
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Project participants: Josh Bongard and Hod Lipson. Please mention both team members when covering this work. Thank you.
Bongard J., Lipson H. (2007),
“Automated reverse engineering of
nonlinear dynamical systems", Proceedings of the National Academy
of Science,
vol. 104, no. 24, pp. 9943–9948
Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate sets of symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the time series of all variables are observable (possibly with some noise). Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system in order to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated “reverse engineering” approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively complex systems in the future.
More Information
Related Publications
Bongard J., Lipson H. (2007), “Automated reverse engineering of nonlinear dynamical systems", Proceedings of the National Academy of Science, vol. 104, no. 24, pp. 9943–9948
Bongard J., Zykov V., Lipson H. (2006), “Resilient Machines Through Continuous Self-Modeling", Science 314(5802): 1118 - 1121
Adami C., (2006) "What Do Robots Dream Of?", Science 314(5802): 1093 - 1094
Application of this concept to other domains:
Aquino W., Kouchmeshky B., Bongard J., Lipson H., (2006) "Co-evolutionary algorithm for structural damage identification using minimal physical testing", Int. Journal for Numerical Methods in Engineering, 69(5): 1085-1107.
Bongard J., Lipson H. (2005) “Active Coevolutionary Learning of Deterministic Finite Automata”, Journal of Machine Learning Research, 6(Oct): 1651-1678.
This project was supported in part by the Keck Future Initiative Grant NAKFI/SIG07. This research was conducted using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, federal agencies, foundations, and corporate partners.